Pour 1 cup room-temperature water into the bowl of a stand mixer. Add 2 1/2 cups all-purpose flour, 1 tablespoon granulated sugar, 1 packet instant yeast, and 1 1/2 teaspoons kosher salt. Mix with the dough hook on low speed until a shaggy dough forms, about 1 minute. Increase the speed to medium-low speed and knead until the dough pulls away from the bowl and is soft, slightly tacky, and can hold a ball shape, for 5 minutes. If the dough looks very sticky, add up to 1/2 cup more flour, 1 tablespoon at a time
Coat a large bowl with cooking spray and add the dough. Cover with greased plastic wrap and let rise in a warm spot until doubled in size, about 1 hour
Line 2 baking sheets with parchment paper. Turn the dough out onto a floured work surface. Divide it into 4 pieces with a bench scraper or knife. Roll each piece into a 16-inch-long and 3/4-inch-thick rope. Cut crosswise into 1-inch pieces, transferring the pieces to the baking sheets as you work
Cover loosely with plastic wrap and let rest in a warm place until puffy, about 20 minutes. Meanwhile, arrange 2 racks to divide the oven into thirds and heat the oven to 425°F. Bring 2 quarts water to a boil in a large pot over high heat
Reduce the heat as needed so the water maintains a simmer and add 1/4 cup baking soda. Working in 3 batches, gently drop the dough into the water, being careful not to overcrowd the pot. Boil for 30 seconds, flip the dough pieces, and boil for 30 seconds more. Remove with a slotted spoon and return to the baking sheets
Whisk 1 large egg with 1 tablespoon water in a small bowl; brush over the dough. Sprinkle with 3 tablespoons coarse sea salt or pretzel salt (about 1 pinch per pretzel bite). Bake until deeply brown and glossy, 13 to 15 minutes
Place 3 tablespoons unsalted butter in a small microwave-safe bowl and microwave in 30-second intervals until melted. Brush over baked pretzel bites and serve warm with cheese sauce if desired